Problem: 7 pencils cost $7.84. Which equation would help determine the cost of 12 pencils?
Answer: There are several equations that could help determine the cost, each with a slightly different approach. We know the cost of 7 pencils. We want to know the cost of 12 pencils. We can write the numbers of pencils as a proportion: $\dfrac{7}{12}$ We know 7 pencils costs $7.84. We can let $x$ represent the unknown cost of 12 pencils. The proportion of these costs can be expressed as: $\dfrac{\$7.84}{x}$ The cost changes along with the number of pencils purchased, and so the two proportions are equivalent. $\dfrac{7}{12} = \dfrac{\$7.84}{x}$